1 Field of the Invention
The present invention generally relates to manipulators and, more particularly, to parallel manipulators moving according to three translational degrees of freedom.
2. Description of the Prior Art
Manipulators have been provided for moving and positioning elements in space, often in response to an output from an automation system. Such manipulators are thus found in various uses, including manipulation of objects in space, supporting and displacing loads, precise displacing of tools, as in the moving tool support of a milling machine.
Serial manipulators are known to have a plurality of links interconnected in series, via joints, to form a chain of links. All joints of a serial manipulator are individually actuated to move an end-effector, often according to the three translational degrees of freedom (X, Y and Z) and the three rotational degrees of freedom (roll, pitch and yaw).
An advantage of serial manipulators resides in the ease of calculating the anticipated position and orientation of its end-effector according to given inputs from the actuated joints of the manipulator. This calculation is known as forward kinematic analysis. Oppositely, the calculation of the necessary inputs of the actuating devices on the links for the end-effector to reach a given position and orientation is known as the inverse kinematic analysis. Serial robots have straightforward forward kinematic analysis leading to a unique solution and, usually, a very complicated inverse kinematic analysis. Parallel manipulators, on the other hand, have, usually, a very complicated forward kinematic analysis and generally (but not always) a straightforward inverse kinematic analysis.
Each link of a chain of links of a serial manipulator must often sustain the entire load supported by the serial manipulator, as well as the weight of the links that are sequentially closer to the end-effector in the chain of links. The links of serial manipulators must be constructed to support such loads, and thus serial manipulators enabled to support heavy loads are themselves heavy. This reduces the load lifting capability of the serial manipulators as a portion of the load comes from its links. Consequently, in existing serial manipulators, heavy loads are constantly set in motion, even when only small and light objects are displaced.
Parallel manipulators provide the advantage of having separate legs sharing the support of a load. Parallel manipulators have a plurality of supporting legs, each separated from one another (i.e., in parallel). Consequently, a load supported by the moving platform is split into smaller loads for each supporting leg. The parallel manipulators are also advantageous in not requiring the actuating devices to be mounted on the links. In many cases, the actuating devices of the parallel supporting members are floor-mounted. Consequently, for a same object to be moved, parallel manipulators involve substantially smaller loads set in motion than would require a serial manipulator.
The complexity of the forward kinematic analysis often precludes the use of parallel manipulators, unless such manipulators involve closed-form solutions, or sufficient computational speed is provided to carry out numerical iterative methods. Closed-form solutions involve solutions based on the solving of polynomials of degree four or less, in which case the solution is readily attained without necessitating numerical iterative methods.
Translational parallel manipulators whose moving platforms are limited to Cartesian movement (i.e., according to three translational degrees of freedom) have been provided in the prior art. The elimination of the three rotational degrees of freedom simplifies the kinematic analyses. Also, for a variety of applications, three translational degrees of freedom are sufficient.
The publication xe2x80x9cStructural Synthesis of Parallel Robots Generating Spatial Translation,xe2x80x9d by J.-M. Hervxc3xa9 and F. Sparacino, reveals the topology of a 2-CRR robot [i.e., a robot having two legs formed serially of a cylindrical joint (C-joint) and two revolute joints (R-joints)]. In the robot of this reference, C-joints have orthogonal axes and are proposed to be actuated. In Section V thereof, there are also notes mentioning that, if a robot with fixed motors is desired, three legs are required.
The publication xe2x80x9cDesign of Parallel Manipulators via the Displacement Group,xe2x80x9d by J.-M. Hervxc3xa9, presents three designs that were chosen from a multitude of possibilities enumerated in xe2x80x9cStructural Synthesis of Parallel Robots Generating Spatial Translation,xe2x80x9d by Hervxc3xa9 and Sparacino. The xe2x80x9cY-Starxe2x80x9d parallel robot, one of the three designs, relates in subject matter to U.S. Pat. No. 4,976,582, issued in 1990 to Reymond Clavel, and entitled xe2x80x9cDevice for the Movement and Positioning of an Element in Space,xe2x80x9d which proposes a popular translational parallel robot (the Delta robot). Another one of the three designs, the xe2x80x9cPrismxe2x80x9d robot is described in xe2x80x9cDesign of Parallel Manipulators via the Displacement Group,xe2x80x9d and has passive prismatic joints (P-joints), i.e., P-joints that are not actuated. Such passive P-joints are quite impractical. It is pointed out that, in xe2x80x9cDesign of Parallel Manipulators via the Displacement Group,xe2x80x9d Herve proposes a generally accurate actuation scheme, stating, however, that the direction of the passive P-joints may be arbitrary, which is wrong. For example, in his xe2x80x9cPrismxe2x80x9d robot, in at least one of the legs with coaxial prismatic actuators, the direction of the passive P-joint should not be perpendicular to the axis of the cylindrical joint (C-joint) of the leg.
The publication xe2x80x9cA Novel Three-DOF Translational Platform and Its Kinematics,xe2x80x9d by T. S. Zhao and Z. Huang proposes a 3-RRC parallel robot with the axes of the C-joints being coplanar. There are two characteristics to this coplanar configuration in the above-mentioned robot: (i) the three translational degrees of freedom of the moving platform cannot be controlled by actuators placed at the C-joints, and (ii) the direct kinematics cannot be solved linearly. The authors do not discuss these drawbacks.
The possibility of using a CRR leg or, more generally, a PRRR leg for constructing a translational parallel robot has not been forgotten in the past. This possibility was mentioned in the publication xe2x80x9cSynthesis by Screw Algebra of Translating In-Parallel Actuated Mechanisms,xe2x80x9d by A. Frisoli, D. Checcacci, F. Salsedo and M. Bergamasco.
In the above publication, researchers have proposed designs with legs having only five R-joints or four passive R-joints and one active P-joint. Initially, the designs included two U-joints (i.e., universal joints), but it became evident that the only requirement should be that, in each leg with five R-joints, the axes of two or three successive R-joints are parallel as well as the axes of the other R-joints, or in each leg with four R-joints and one P-joint, the axes of two successive R-joints or two R-joints connected via a P-joint are parallel, while the axes of the other two R-joints are also parallel. An example of this is also illustrated in xe2x80x9cA Family of 3-DOF Translational Manipulators,xe2x80x9d by M. Carricato and V. Parenti-Castelli.
The publication xe2x80x9cKinematic Analysis of Spatial Parallel Manipulators: Analytic Approach,xe2x80x9d by Doik Kim proposes a number of new generalized translational parallel mechanisms. One of the proposed architectures is based on three PRRRR legs. In each leg, the axes of the last three R-joints are mutually parallel but not parallel to the direction of the P-joint, and the second R-joint is skew to both the direction of the P-joint and the axes of the other three R-joints.
Finally, U.S. Pat. No. 5,156,062, issued in 1992 to Walter T. Appleberry, entitled xe2x80x9cAnti-Rotation Positioning Mechanism,xe2x80x9d discloses a 3-URU (or 3-UPU) translational parallel mechanism.
In the creation of a manipulator, two factors are opposed. On one hand, the moving platform of the manipulator must be displaceable as freely as possible, with regard to the six degrees of freedom. On the other hand, the displacement of the moving platform must be readily calculable. One way to simplify this calculation is to constrain the moving platform to Cartesian movement by specific arrangements of the joint axes and proper selection of the joints to be actuated.
It is therefore an aim of the present invention to provide a translational parallel manipulator having a movable portion whose position is calculable in space according to the solution of a set of linear equations.
It is a further aim of the present invention to provide a method for controlling a displacement of the movable portion of the translational manipulator.
It is a still further aim of the present invention to provide a decoupled translational parallel manipulator.
It is a still further aim of the present invention to provide an isotropic decoupled translational parallel manipulator.
Therefore, in accordance with the present invention, there is provided a manipulator for receiving and displacing an object, comprising a moving portion, adapted for receiving the object; at least three articulated support legs each extending between the moving portion and a ground for supporting the moving portion, each of the articulated support legs being connected to the ground by a first joint member and to the moving portion by a second joint member, the first joint member and the second joint member in each of the articulated support legs being interconnected by at least a third joint member, the articulated support legs each having at least one rotational degree of freedom and having constraints in the joint members operable to restrict movement of the moving portion to three translational degrees of freedom and to constrain a relationship between linear displacement of the first joint members and output of the moving portion to be linear; and at least three linear actuators being each operatively connected to a different one of the first joint members for controlling the movement of the moving portion in any of the three translational degrees of freedom.
Also in accordance with the present invention, there is provided a method for controlling movement of a moving portion of a manipulator in any of three translational degrees of freedom, comprising the steps of providing a manipulator having a moving portion being supported by at least three articulated support legs each extending between the moving portion and a ground, each of the articulated support legs being connected to the ground by a first joint member and to the moving portion by a second joint member, the first joint member and the second joint member of each of the articulated support legs being interconnected by at least a third joint member, the articulated support legs each having at least one rotational degree of freedom and having constraints in the joint members operable to restrict movement of the moving portion to three translational degrees of freedom and to constrain of the relationship between linear displacement of the first joint members and output of the moving portion to be linear; providing at least three linear degrees of actuation to the manipulator by connecting an actuator to each of the first joint members; receiving a displacement signal for a given position of the moving portion; calculating control signals for the actuators of the first joint members using a linear function of said displacement signal; and displacing the moving portion to the given position by controlling the three degrees of actuation in accordance with said control signals.